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Trumpet vines take a few years to reach maturity and bloom, so sadly you'll just have to wait for now.

You can read more about trumpet vine flowering here:
https://www.gardeningknowhow.com/ornamental/vines/trumpet-vine/trumpet-vine-no-blooms.htm

Glad you found the article useful.

I think you have two options. You could select several strong, straight shoots that are growing now, and cut off the rest of the shoots at the base. Or, you could wait until fall and cut the whole plant back to 0-8 inches from the ground and essentially start again next spring, then proceed as if the plant is 2 years old instead of 3 next year. It does look like you have several good, strong shoots now, so going with the first option should work.

I'd recommend waiting to see if some sprouts grow from the root ball. Trumpet vines, if well established, are pretty tough, even when trimmed radically. The vine might still make it.

The most common reason is that the vine is not old enough, it can take 10 years for a vine to bloom.
This link will help you determine the cause.

https://www.gardeningknowhow.com/ornamental/vines/trumpet-vine/trumpet-vine-no-blooms.htm

I agree that there seems to be no signs of life or growth in the 2nd vine.

Are the stems pliable when you bend them? Do they snap and break? Dead stems will break right off.

If the stems still bend, be patient and give the vine more time.

Here is an article to refresh you on the care requirements.

https://www.gardeningknowhow.com/ornamental/vines/trumpet-vine/growing-trumpet-vines.htm

This article will help you.

https://www.gardeningknowhow.com/ornamental/vines/trumpet-vine/bugs-on-trumpet-vines.htm